Consider the function $f:C^2\rightarrow C$ and it is defined by:


where $R(z_a)$ is the real part of $z_a$ and $I(z_b)$ is the imaginary part of $z_b$.

Can I write $f(z_a,f(z_b,z_c))=f(f(z_a,z_b),z_c)$ in this case?

I spotted where I went wrong.

My working:


I have accidentally put down $f(z_a,f(z_b,z_c))=R(z_a)+iI(z_b)$ but still got $f(f(z_a,z_b),z_c)=R(z_a)+iI(z_c)$ in my previous working so my LHS is not same as RHS and could not find out the mistake by reading thought my handwriting. But once I typed it up, I spotted it.

So this equation is correct.

  • 1
    $\begingroup$ That property is called "associativity". Also, here on MSE it's very good to show your work and where you got stuck. $\endgroup$ – Richard Nov 1 '18 at 18:04
  • $\begingroup$ Thanks for your advice, and I literually spotted my mistake by typing my working up. Thank! $\endgroup$ – BlackSky Nov 1 '18 at 18:16

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